Computational Mathematics, Fall '12 (124)

Let us reflect that, having banished from our land that religious intolerance under which
mankind so long bled and suffered, we have yet gained little if we countenance a political
intolerance as despotic, as wicked, and capable of as bitter and bloody persecutions.
  — Thomas Jefferson (1743-1826) in his First Inaugural Address

Homework List

✈ Jump down to 'This Week.'

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Week 1

• Wednesday, Aug 22 — First day of class
  Read Chapter 1. 'What is Numerical Analysis?'
  
  
• Friday, Aug 24
  "Computer Arithmetic," Exercises 2 → 4.
  

Week 2

• Monday, Aug 27
  "Computer Arithmetic," Exercises 6 → 7.
  Numerical Analysis, pg 8: No 16, 17, 18, 26, 27. Look at: 21, 22.
  
  
• Wednesday, Aug 29
  "Computer Arithmetic," Exercises 8 → 10.
  Numerical Analysis, pg 14: No 42.
  
  
• Friday, Aug 31
  ¤ Compare the different rounding methods.
  ¤ Why is "Round to nearest, ties to even" selected as the default method?
  

Week 3

• Monday, Sept 3
  ☀ No classes — Labor Day
  
  
• Wednesday, Sept 5
  "Computer Arithmetic," Exercises 15, 16.
  Numerical Analysis, pg 5: No 1.3, 1.4, 1.8, 1.9. Compare (pg 11) 1.26 and 1.27.
  
  
• Friday, Sept 7
  "Computer Arithmetic," Exercises 17, 18.
  Numerical Analysis, pg 100: No 12.14 (carefully read the problem's solution).
  
  

Week 4

• Monday, Sept 10
  "Control Structures," Exercises 1a, 2a.
  
  
• Wednesday, Sept 12
  ◊ The 'Collatz Conjecture Project' from class projects.
  ¤ A sample of producing a point-plot with Maple.
  "Control Structures," Exercise 3.
  
  
• Friday, Sept 14
  ¤ The project is due today.
  "Control Structures," Exercises 4.
  
  

Week 5

• Monday, Sept 17
  "Control Structures," Exercises 1b-d, 5.
  
  
• Wednesday, Sept 19
  ◊ Write an if-then statement that tests whether the value of \(f(x)=\cos(x)\) is positive in
  1. Maple
  2. Matlab
  3. Java
  4. TI-84
     giving \(f(x)\) if yes and no result if no.
  ◊ Write a loop that computes the value of \(g(x)=\sin(x)\) at 11 equally spaced points from 0 to \(2\pi\) in
  1. Maple
  2. Matlab
  3. Java
  4. TI-84
  
  
• Friday, Sept 21
  "Control Structures," Exercise 11.
  
  

Week 6

• Monday, Sep 24
  ◊S 1: Horner's method Exercise 3, 5, LA 6.
  ¤ Cf: Numerical Analysis, pg 187: No 18.5.
  
  
• Wednesday, Sep 26
  ¤ Review day:
     — Study for the test!
  
  
• Friday, Feb 28
  ◊ Test today!
  ¤ Test 1 Topics
     — Remember to bring your one-page 'notes sheet.'
  
  

Week 7

• Monday, Oct 1
  "Numerical Differentiation," Exercise 4a, 5a.
  Numerical Analysis, pg 111: No 13.5, 13.7.
  
  
• Wednesday, Oct 3
  "Numerical Differentiation," Exercise 3, 4, 5; Look at 9.
  
  
• Friday, Oct 5
  ¤ Examine the table of repeated differences for \(f(x)=e^x\) comparable to what we did in class.
       Spoiler alert! Maple worksheet.
  
  

Week 8

• Monday, Oct 8
  ¤ Apply the bisection method to \(p(x)=-x^9+x^2+x+\frac13\) using Cauchy's root bound to find a starting interval.
  ¤ Apply the bisection method to \(f(x)=e^{(2-x)}-x\) with a suitable starting interval.
  
  
• Wednesday, Oct 10
  ◊ Look up the history of the bisection method.
  
  
• Friday, Mar 9
  ◊ Fall Break — no classes
  ¤ Last day to register to vote for the upcoming election.
  ◊ Let's be careful out there! — Sgt Esterhaus
  
  

Week 9

• Monday, Oct 15
  ◊ Look up the history of the Newton-Rapheson method.
  
  
• Wednesday, Oct 17
  ◊ Root Finding Algorithms Exercise 1, 2, 3, 5.
  ¤ Numerical Analysis, pg 333: No 25.10.
  
  
• Friday, Oct 19
  ◊ Root Finding Algorithms Exercise 1, 2, 3, 5 with the Secant method.
  
  

Week 10

• Monday, Oct 22
  ◊ Root Finding Algorithms Exercise 6 with the bisection, Newton, and secant methods.
  ¤ The Maple root finding methods worksheet.
  
  
• Wednesday, Oct 24
  ◊ Root Finding Algorithms Exercise 7 with the bisection, Newton, and secant methods.
  ¤ Test 2 Topics List.
  ¤ Build your formula sheet for the test.
  
  
• Friday, Oct 26
  ◊ Test today!
  
  

Week 11

• Monday, Oct 29
  ◊ Root Finding Algorithms: Exercise 7 using Regula Falsi.
  
  
• Wednesday, Oct 31
  ◊ Numerical Integration: Exercise 1.
  
  
• Friday, Nov 2
  ¤ ProjectDay — no formal class
  ◊ Projects, Root Finding:
    — Choose either "Commissioner Loeb’s Demise" or "Bernoulli’s Method and Deflation". Reports are due Monday, Nov 5.
  
  

Week 12

• Monday, Nov 5
  ◊ Numerical Integration: Exercise 3.
  
  
• Wednesday, Nov 7
  ◊ Numerical Integration: Exercise 4 (just with Gaussian quadrature).
  ¤ Cf: Numerical Analysis, pg 122: No 14.4, 14.10.
  
  
• Friday, Nov 9
  ◊ Numerical Integration: Exercise 4 (just with Gaussian quadrature using Excel).
  
  

Week 13

• Monday, Nov 12 — Veteran's Day Be sure to thank them!
  ◊ Numerical Integration: Fill in the "Class Exercise" blanks on pg 119.
  
  
• Wednesday, Nov 14
  ◊ Numerical Integration: Exercise 2, 4.
  
  
• Friday, Nov 16
  ¤ Test 3 — due Monday, Nov 26, in class.
  
  

Week 14

• Monday, Nov 19
  ◊ Lagrange Interpolation: Exercise 1 (just with Lagrange interpolaton).
  ¤ A Maple worksheet demo of Lagrange Interpolation.
  
  
• Wednesday, Nov 21
  ◊ Thanksgiving Break — no classes
  
  
• Friday, Nov 23
  ◊ Thanksgiving Break — no classes
  
  

Week 15   ♞  (This Week)

• Monday, Nov 26
  ¤ Determine why the sets of knots
  1. \(K_1=\{x_k=k\cdot\pi\}\) for \(k=0..n\)
  2. \(K_2=\{x_k=(4k+1)\cdot\pi/2\}\) for \(k=0..n\)
  are very bad choices.
  
  
• Wednesday, Nov 28
  
  
• Friday, Nov 30
  
  

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“On two occasions I have been asked, ‘Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?’ ... I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.”

Last modified: Wednesday, 01-Feb-2023 08:32:12 EST

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